论文标题
关于一维固定schrödinger方程的多尺度不连续galerkin方法的共振误差的数值调查
Numerical investigations on the resonance errors of multiscale discontinuous Galerkin methods for one-dimensional stationary Schrödinger equation
论文作者
论文摘要
在本文中，进行了数值实验，以研究数值迹线中的罚款参数对高阶多尺度不连续的盖尔金（DG）方法的共振误差[6，7]对一维固定固定schrödinger方程的影响。先前的工作表明，惩罚参数必须在误差分析中为正，但是零惩罚参数的方法在粗网格的数值模拟中效果很好。在这项工作中，通过执行广泛的数值实验，我们发现零惩罚参数会导致多尺度DG方法中的谐振错误，并且采用正惩罚参数可以有效地减少共振错误并使全球线性系统中的矩阵具有更好的条件数量。
In this paper, numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high order multiscale discontinuous Galerkin (DG) methods [6, 7] for one-dimensional stationary Schrödinger equation. Previous work showed that penalty parameters were required to be positive in error analysis, but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes. In this work, by performing extensive numerical experiments, we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods, and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.
